Name___________________________
Algebra 8, Unit 2: Lesson 14 – Unit test Review
Multiple Choice: Select the choice that best represents the answer to the question.
1. Give the domain and range of the relation {(1, −8), (−7, 8), (−3, 7), (−3, −5)}.
(1)
D: {7, 8, −8, −5}
R: {−3, −7, 1}
(2)
D: {−3, −7, 1, 3}
R: {7, 8, −8, −5}
(3)
D: {−3, −3, −7, 1}
R: {7, 8, −8, −5}
(4)
D: {−3, −7, 1}
R: {7, 8, −8, −5}
Use the graph to the right to answer #2 and #3.
2. Identify the interval where the function is decreasing.
(1) (0, 3)
(2) [−1, 0]
(3) (−1, 0)
(4) (−∞, −1) ∪ (3, ∞)
3. Determine the range of the function.
(1) (−∞, ∞)
(2) [0, 4]
(3) (0, 4)
(4) [−1, 3]
4. What is a formula for the nth term of sequence 10, 12, 14, 16 ?
(1) 𝐴𝑛 = 10(2)𝑛
(2) 𝐴𝑛 = 10(2)𝑛−1
(3) 𝐴𝑛 = 10 + 2𝑛
(4) 𝐴𝑛 = 10 + (𝑛 − 1)(2)
5. Given g ( x)   x 2  4 x  4 , find the value for g (3) .
(1) 3
(3) 11
(2) -1
(4) -17
6. Is the sequence arithmetic? If so, identify the common difference.
14, 21, 42, 77, ...
(1) yes, 7
(3) yes, 14
(2) yes, −7
(4) No
7. Find the two-hundredth term of the sequence 2, 5, 8, 11…..
(1) 399
(3) 599
(2) 499
(4) 603
9. Which of the following has a common difference?
(1) -5, -19, -33, -46
(2) -6,-18, -54, -162
(3) -5, -19, -33, -47
(4) -6, 18, -54, 162
10. The first term of an arithmetic sequence is 𝑎1 = 3 and the eleventh term is 23. Find the equation
of the sequence.
(1) 𝑎𝑛 = 23 + 2(𝑛 − 1)
(2) 𝑎𝑛 = 3 + 2(𝑛 − 1)
(3) 𝑎𝑛 = 3(10)𝑛−1
(4) 𝑎𝑛 = 3 + 10(𝑛 − 1)
Short Answer
11. Write the first 3 terms in the following sequences. Identify them as arithmetic or not arithmetic.
a) 𝐴(𝑛 + 1) = 𝐴(𝑛) − 5 for 𝑛 ≥ 1 and 𝐴(1) = 9.
1
b) 𝐴(𝑛 + 1) = 2 𝐴(𝑛) for 𝑛 ≥ 1 and 𝐴(1) = 4.
12. Write the explicit rule and the recursive rule for the following sequences:
a) −2, 2, 6, 10 …
1
1
b) 1, 2 , 0, − 2 …
13. Graph 𝑓(𝑥) = −3𝑥 + 2, for
{𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 − 2 ≤ 𝑥 ≤ 2}.
x
y
Is this function discrete or continuous?
Explain.
14. Determine the domain and range of each of the functions below. Show answer for part a in
interval notation and answer for part b in and set notation.
a)
15.
b)
Determine if the following relations are functions. Justify your answer.
a) {(1, −5), (3, 9), (4, 5), (7, 8), (12, −8)}
b)
16. Determine the rate of change from the following intervals for the graph below:
a) 0 ≤ 𝑥 ≤ 2
b) 4 ≤ 𝑥 ≤ 8
c) Which of the above rates of change is the faster rate? Explain your answer.
17. Function Analysis: Use the graph below to answer each of the following questions.
a. Is the graph a function? Explain why or why not.
b. State the domain using interval notation.
c. State the range in interval notation.
d. Identify the interval(s) where the graph is increasing.
e. Identify the interval(s) where the graph is decreasing.
f. Identify the interval(s) where the graph is positive.
g. Identify the interval(s) where the graph is negative.
h. State the coordinates of the x-intercept(s).
i. State the coordinates of the y-intercept.
j. Label any relative maxima with an A and relative minima with a B.
18.
Graph the following piecewise function. Show all necessary work.
1 2
𝑥 + 1,
𝑥<2
𝑓(𝑥) = { 2
2,
2≤𝑥<5
1 − 𝑥,
5<𝑥≤9
19. Determine the equation of piecewise function graphed below. Show all necessary work.
Evaluating Functions Questions 23-25:
20. Given the functions f ( x)  x 2 and g ( x)  5 x  x , find each of the following.
a. g (5)
b. f (3)
c. 𝟐𝒈(𝟖)
d.
f ( a  2)
21. Find the third term in the recursive sequence, 𝐴(𝑛 + 1) = 2𝐴(𝑛) − 1, where 𝐴(1) = −2.
22. The Math Club sells hot dogs at a school fundraiser. The club earns $108 and has a combination
of five-dollar and one-dollar bills in its cash box.
a) Write an equation to model this situation.
b) Explain each variable used in the equation. Explain the meaning of the x and y intercepts.
c) Graph the equation and label appropriately.
23. What are the x and y intercept for the following equation? Show algebraically.
3x – 4y = 12
24. If 𝐟 is defined 𝐟: 𝐗 → 𝐘 and 𝐟 = {(𝟐, 𝟒), (−𝟐, 𝟐), (𝟒, 𝟔), (𝟐, 𝟏)},
(a) Draw a mapping diagram to represent this relation.
(b) What is the domain of 𝐟?
(c) What is the range of 𝐟?
(d) Is this relation a function? Explain why or why not?
25. Based on the graph below, answer each of the following questions:
a) State the domain in interval notation.
b) State the range in interval notation.
c) Is the graph a function?
0
d) Is the graph continuous or discrete?
e) State the intervals of increasing and decreasing.
f) State the intervals of positive and negative.
26. Using the piecewise function to the right answer the following questions:
a) Write the equation for the following piecewise.
b) State the domain in interval notation.
c) State the range in set notation.
27. Find the average rate of change on the interval 2  x  5 , for the equation y   x 2  2 x  3 .
28. A sequence has A(11) = 20 and d = -3, find the 30th term.
29. Find the equation of line that passes through (-1, 2.2) and (-5, 10.2).
30. Consider the sequence: 9, 1, −7, −15, ….
a. Describe the pattern in words
b. Write a recursive formula for the sequence.
c. Write an explicit formula for the sequence.
c. Find the 57th term of the sequence.
31. If −6, a, b, c, −82 forms an arithmetic sequence, find the values of a, b, and c?